Existence Results for Singular Boundary Value Problems on Unbounded Domains in Banach Spaces (original) (raw)
Mathematics and Computer Science, 2017
We considering the problem of solving a nonlinear differential equation in the Banach space of real functions and continuous on a bounded and closed interval. By means of the fixed point theory for a strict set contraction operator, this paper investigates the existence, nonexistence, and multiplicity of positive solutions for a nonlinear higher order boundary value problem.
Existence of Positive Solutions for Singular Second-orderm-Point Boundary Value Problems
Acta Mathematicae Applicatae Sinica, English Series, 2004
In this paper we consider the existence of at least one positive solution to a class of singular semipositone coupled system of nonlocal boundary value problems. We show that the system possesses at least one positive solution by using fixed point index theory. We remark that to some extent our systems and results generalize and extend some previous works.
Journal of Computational and Applied Mathematics, 1993
This paper is concerned with the existence and uniqueness of solution of a class of two-point singular nonlinear boundary value problems. It is shown that the problem has a unique solution only for certain boundary conditions under the assumption that the range of af /ay has empty intersection with the closure of the spectrum of the singular differential operator, where f denotes the nonlinearity.
Existence of positive solutions for a nonlinear third order boundary value problem
Advances in Fixed Point Theory, 2012
This work concerned withthe following third-order three point boundaryvalue problem (BVP). Our main objective is to investigatethe existence, uniqueness and existence of positive solutions forthe boundary value problem (P1), by using Banach contractionprinciple, Leray Schauder nonlinear alternative, properties of theGreen function and Guo-Krasnosel'skii fixed point theorem in cone,in the case where the nonlinearity fff is either superlinear orsublinear.
Existence Results for Some Initial- and Boundary-Value Problems
Proceedings of the American Mathematical Society, 1990
In this paper, using the Schauder Fixed Point Theorem, we establish some existence results or initial and boundary value problems for differential equations withouth growth restriction on the right member.
Positive solutions to a singular second order boundary value problem
International Journal of Mathematical Analysis, 2013
In this paper, we investigate the existence and multiplicity of positive solutions for a singular second order scalar Sturm-Liouville boundary value problem with different values of λ for a function f involve u by applying the Krasnosel'skii fixed point theorem on compression and expansion of cones.
2010
In this manuscript we study initial value problems and boundary value problems for a first order ordinary differential equations. We establish the existence of solutions by the Banach Contraction Mapping Principals. Next we present the numerical methods for the above initial value problems, where the numerical comparison between the Euler and Runge-Kutta methods are being investigated. We prove the existence of solutions to the multipoint by Schaeffer fixed point theorem and uniqueness of solutions by the Contraction Mapping Principal.